By "support" from the employer, I think Mrs Doolittle might have meant not only organisational advice and help, but also financial support, for example

• to pay for a relocation agent, so that money does not come out of your pocket
• to pay for a furnished appartment, such as Swiss Star or similar, for the first month for you alone, and at some point later for your family, too, for a pre-agreed number of months
• to pay for the moving expenses when your family, and all your possessions, move to Switzerland.

An alternative is that the company provides you with a flat budget amount, for the whole move, for you to spend as you choose. If you know whether that's even an option, and how much, it will give you a better basis for planning.

I agree with Mrs Doolittle: first get yourself a furnished room with a short notice period.

Then, travel up and down all the public transport routes in the city, or cycle, to get a feel for the way things work. There are no really, really bad areas.

Do not be discouraged if you apply for apartments and don't even hear back from them. Other than in the top, luxury segment, there are many, many applicants for each flat, and the offices which receive them simply cannot reply to each person they turn down.

Try to get your application bundle together, so you an apply online. Include the following two:

• One of the central documents needed, here, is called a "Betreibungsauszug" which, of course, you cannot have, as you come from abroad. If, where you are now, there is any official government paper which certifies that you do not have any debt, then definitely get that, and have it translated. If your current country does not have such a document, then ask your bank manager to certify that your accounts are correctly run, that you have not been in bad debt (by "bad" meaning you have defaulted on a repayment).
  
• If you are tenant where you live now, ask your landlord for a letter stating how long you lived in his/her building, that you always paid punctually (hope that's true) and that you were a good tenant who caused no trouble (ditto, true).

When you apply for a flat, if there is space in the application, briefly mention all of the following, if they are true:

• I am an EU-citizen employed in Schaffhausen
• my finances are in proper order
• we are respectful of the building and neighbours
• no-one in my family smokes.

Write in German.
When you get a contract, before you sign make sure you understand it, especially the notice period, just in case you think it is a fine place to live, but it later turns out not to be suitable for your wife and children.